Example 4.5.1.12. Let $F: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{D}}$ be a functor between categories. Then the induced map $\operatorname{N}_{\bullet }(F): \operatorname{N}_{\bullet }(\operatorname{\mathcal{C}}) \rightarrow \operatorname{N}_{\bullet }(\operatorname{\mathcal{D}})$ is an equivalence of $\infty $-categories if and only if $F$ is an equivalence of categories.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$